22065 ÷ 4 = 5516 R1
Alright, let's work through the division of 22065 by 4 step by step.

Step 1:
4 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 4

Step 2:
4 goes into 22 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 20 from 22 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 4

Step 3:
4 goes into 20 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 55
Subtract 20 from 20 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 4:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 551
Subtract 4 from 6 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 4

Step 5:
4 goes into 25 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 5516
Subtract 24 from 25 to get 1.

The final result is 5516 with a remainder of 1.